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\contentsline {chapter}{List of Figures}{iv}
\contentsline {chapter}{List of Tables}{v}
\contentsline {chapter}{Abbreviations and Symbols}{ix}
\contentsline {chapter}{\numberline {1}Introduction}{3}
\contentsline {section}{\numberline {1.1}Overview}{3}
\contentsline {section}{\numberline {1.2}Motivations}{4}
\contentsline {section}{\numberline {1.3}Outline of the chapters}{5}
\contentsline {chapter}{\numberline {2}Statistical learning}{7}
\contentsline {section}{\numberline {2.1}Introduction}{7}
\contentsline {section}{\numberline {2.2}Machine learning}{7}
\contentsline {section}{\numberline {2.3}Learning process}{9}
\contentsline {section}{\numberline {2.4}Risk functional}{9}
\contentsline {section}{\numberline {2.5}Empirical risk minimization principle}{11}
\contentsline {section}{\numberline {2.6}VC dimension}{13}
\contentsline {section}{\numberline {2.7}Structural risk minimization principle}{14}
\contentsline {section}{\numberline {2.8}Conclusion}{16}
\contentsline {chapter}{\numberline {3}Support Vector Machines}{17}
\contentsline {section}{\numberline {3.1}Introduction}{17}
\contentsline {section}{\numberline {3.2}SVMs with hard margins}{18}
\contentsline {section}{\numberline {3.3}SVMs with soft margins}{20}
\contentsline {section}{\numberline {3.4}Implicit mapping using kernel functions}{23}
\contentsline {section}{\numberline {3.5}An example}{25}
\contentsline {section}{\numberline {3.6}Conclusion}{26}
\contentsline {chapter}{\numberline {4}Training SVMs}{27}
\contentsline {section}{\numberline {4.1}Introduction}{27}
\contentsline {section}{\numberline {4.2}Optimality conditions and feasible regions}{28}
\contentsline {section}{\numberline {4.3}Training methods for SVMs}{29}
\contentsline {subsection}{\numberline {4.3.1}Classical methods}{29}
\contentsline {subsection}{\numberline {4.3.2}Geometric methods}{30}
\contentsline {subsection}{\numberline {4.3.3}Iterative methods}{31}
\contentsline {subsubsection}{\numberline {4.3.3.1}Gradient ascent}{31}
\contentsline {subsubsection}{\numberline {4.3.3.2}Successive Over Relaxation}{34}
\contentsline {subsection}{\numberline {4.3.4}Working set methods}{38}
\contentsline {subsubsection}{\numberline {4.3.4.1}QP sub-problem}{38}
\contentsline {subsubsection}{\numberline {4.3.4.2}Chunking}{40}
\contentsline {subsubsection}{\numberline {4.3.4.3}$\mathrm {SVM}^{light}${}}{40}
\contentsline {subsubsection}{\numberline {4.3.4.4}Sequential Minimal Optimization}{41}
\contentsline {subsection}{\numberline {4.3.5}Boosting methods}{48}
\contentsline {subsubsection}{\numberline {4.3.5.1}The SVM-EDR training algorithm}{48}
\contentsline {section}{\numberline {4.4}Conclusion}{52}
\contentsline {chapter}{\numberline {5}SVMBR program overview}{53}
\contentsline {section}{\numberline {5.1}Introduction}{53}
\contentsline {section}{\numberline {5.2}Internal structure}{53}
\contentsline {section}{\numberline {5.3}Using SVMBR}{54}
\contentsline {section}{\numberline {5.4}SVMBR use summary}{58}
\contentsline {chapter}{Bibliography}{71}
\contentsfinish 
